722 



NATURE 



[February 3, 192 1 



The subject of intratracheal insufflation of ether 

 is fully dealt with, and perhaps that of intravenous 

 ether infusion receives more space than it deserves, 

 as some of its leading exponents seem now to 

 use it but little. This may be due to the more 

 • extende"d use of rectal etherisation combined with 

 oil, which, although a little troublesome, has 

 proved very useful in plastic surgery about the 

 head, and especially in bad cases of Graves' 

 disease. 



Many subjects concerning which it has been 

 difficult to obtain a connected account without 

 reference to the original papers are clearly and 

 sufficiently summarised in this edition. Among 

 these, one notices the sections dealing with 

 acapnia, anoci-association, acidosis, and shock 

 with its allied conditions. Dr. Buxton is certainly 

 to be congratulated on having not only modern- 

 ised, but also improved what was already one of 

 the very best text-books on the subject. 



Mathematical Text-books. 



(i) An Elementary Treatise on Differejitial Equa- 

 tions and their Applications. By Prof. H. T. H. 

 Piaggio. (Bell's Mathematical Series. .'Ad- 

 vanced Section.) Pp. xvi-t- 2i6-t-xxv. (London: 

 G. Bell and Sons, Ltd., 1920.) Price i2i-. net. 



(2) Elementary Algebru. Part i. By C. V. Durell 

 and G. W. Palmer. (Cambridge Mathematical 

 Series.) Pp. viii-l-256-fxlvi. (Answers.) 

 (London: G. Bell and Sons, Ltd., 1920.) With 

 introduction, price 4s. 6d. ; without introduc- 

 tion, price 35. 6d. 



(3) A Short Course in College Mathematics : Com- 

 prising Thirty-six Lessons on Algebra, Co- 

 ordinate Methods, and Plane Trigonometry. By 

 Prof. R. E. Moritz. Pp. ix -H 236. (New York : 

 The Macmillan Co. ; London : Macmillan and 

 Co., Ltd., 1919.) Price los. 6d. net. 



(4) Arithmetic. Part ii. By F. W. Dobbs and 

 H. K. Marsden. (Bell's Mathematical Series.) 

 Pp. xii-l- i63-(-xi. (Answers.) (London: G. Bell 

 and Sons, Ltd., 1920.) Price 35. 6d. 



(i) /"^F the two volumes that head the list it 

 V^ is difficult to speak too highly. The 

 scope of that on differential equations is stated 

 most succinctly to teachers by the mere state- 

 ment that it covers the course for the London 

 B.Sc. Honours, Schedule A of the second part 

 of the Tripos, and some of the work for the 

 London M.Sc. and for the Tripos, part ii. The 

 author has clear views of the equipment of the 

 students who are likely to use the book — an ele- 

 mentary knowledge of the differential and integral 

 calculus, and a little co-ordinate geometry. In 

 NO. 2675, VOL. 106] 



the old days it was quite possible for a respectable 

 mathematician to become, with comparatively little 

 effort, also a respectable mathematical physicist. 

 Owing to the remarkable extension of specialisa- 

 tion in both subjects, this is no longer the case. 

 It is perhaps all the more essential that the living 

 interest of such a branch of the subject as this 

 should be maintained at every stage, and it is 

 here that the crucial test is made of the powers 

 of the mathematician who also aspires to be a 

 great teacher. He is not content merely to "give 

 an account of the central parts of the subject in as 

 simple a form as possible." He is careful that 

 the various stages of the journey shall lead to 

 Pisgah heights from which may be viewed the 

 Promised Land to which the adventurous may 

 make their way, and some province or other of 

 which, according to taste or opportunity, they may 

 some day make their own. Nor are the names and 

 records of the older guides forgotten, and as each 

 fresh height is scaled historical notes give just 

 enough to fix the chronology and to whet the 

 apjjetite for further information about those who 

 first made their own the notable peaks and crags 

 around the young climber. 



In the first chapter we are glad to see the in- 

 fluence of the remarkable chapters published by 

 Dr. Brodetsky last year in the Mathematical 

 Gazette, and of Prof. Wada's paper on 

 graphical solution. Chap, iv., on simple partial 

 differential equations, with their genesis, the con- 

 struction of simple particular solutions, and the 

 procedure from simple to complex solutions with 

 the help of Fourier's series, is a welcome innova- 

 tion at so early a stage. 



Chap, vi., on singular solutions, abandons any 

 attempt at an analytical treatment at this stage 

 of the student's development, and appeals to geo- 

 metrical intuition. Chap. ix. deals with solution 

 in series, following the method of Frobenius- 

 Here we find among the examples the equations 

 associated with the names of Bessel, Legendre, 

 and Riccati, with a sketch of the hypergeometric 

 equation and its twenty-four solutions. The 

 nature of an existence theorem is explained in 

 chap. X. The methods of Picard and Cauchy are 

 followed by a discussion of the method of Fro- 

 benius, and here plentiful references are given for 

 the benefit of those whose knowledge of the theory 

 of series is inadequate. The references, indeed, 

 are plentiful throughout. We may note one that 

 is of little use to many of us — Stodola's "Steam 

 Turbine," which has been unobtainable for some 

 time past. In the miscellaneous examples the 

 author, in a large number of cases, adds to the 

 theorems to be solved the physical applications. 



